Be definition:VJesus12 wrote:$$\text{Is}\ \ \ \sqrt{\left(y-4\right)^2}=4-y\ \ ?$$
(1) |y-3| less than or equal to 1
(2) y*|y|>0
√(x²) = |x|.
|x-y| is the DISTANCE between x and y.
Thus, √(y-4)² = |y-4| = the distance between y and 4.
Question rephrased: Is |y-4| = 4-y?
In other words:
Is the DISTANCE between y and 4 equal to the DIFFERENCE between 4 and y?
A DIFFERENCE can be negative, 0, or positive.
A DISTANCE must be greater than or equal to 0.
For the DIFFERENCE between two values to be equal to the DISTANCE between the two values, the DIFFERENCE -- like the DISTANCE -- must be greater than or equal to 0:
4-y≥0
y≤4.
Question rephrased: Is y≤4?
Statement 1: |y-3|≤ 1.
-1 ≤ y-3 ≤1
2 ≤ y ≤ 4
Since y must be between 2 and 4, inclusive, it must be less than or equal to 4.
SUFFICIENT.
Statement 2: y|y|>0 .
Since |y| cannot be negative, the left-hand side must be (+)(+).
Thus, y > 0.
Since it's possible that y<4, y=4, or y>4, INSUFFICIENT.
The correct answer is A.
